So, ffmpeg, used by HandySaw, in this case creates file in MPEG-1 format. It selects format accordingly destination file extension. And here destination file has same extension as source.
Usually it is not a problem but in this case VLC cannot normally playback such files.
I can propose several workarounds:
1. Change extension of source file to .TS - this is unambiguously MPEG-2 Transport Stream format. Despite source format still is MPEG-2 ffmpeg will read it and create result in correct MPEG-2 Transport Stream format. VLC plays it correctly.
2. I created copy of "Direct Stream Copy" FFmpeg Engine preset and named it "Direct stream copy MPEG-2 PS". It is in attachment. Place it in HandySaw installation folder. In it I've added output format setting "-f dvd", so this preset will copy any source media regardless its format to MPEG-2 PS format files.
Of course do not forget to select it in HandySaw Preferences